Let M = 〈M, +, λЄDλЄD〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex V-definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L.

2020-05-13T18:02:39ZGroups definable in ordered vector spaces over ordered division ringsStarchenko, Sergeiterms-of-useEleftheriou, Pantelis E.2014-03-12Let M = 〈M, +, <, 0, {λ}<sub>λЄD</sub>λЄD〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, e<sub>G</sub>〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex V-definable subgroup U of 〈M<sup>n</sup>, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L.2020-05-13T18:02:39ZEleftheriou, Pantelis E.Starchenko, Sergeieng